A machine-learning and data assimilation forecasting framework for surface waves

Abstract

In this article, we combine deep symbolic regression (DSR) and ensemble optimal interpolation-based data assimilation (DA) methods to correct the error in forecasts from the numerical model WaveWatch III. In our experiments, DA and DSR training is performed on hindcasts and then the model is integrated forward in time using both the numerical model and the symbolic expressions generated from the DSR procedure to generate the forecasts. The DSR method is utilized in this article to generate the symbolic equations that correct the model error in the WaveWatch III/ DA system. The proposed algorithm takes the zonal ((Formula presented.)) and meridional ((Formula presented.)) wind components from Global Forecast System (GFS) forecasts, wave heights from WaveWatch III, and geographical coordinates (latitude and longitude) to model physical relationships not included in the original numerical model. The DA is performed using Jason-2 and Satellite with ARgos and ALtiKa (SARAL) altimeter measurements, and the independent testing uses in situ buoys. The root-mean-squared deviation (RMSD) of the proposed method is better than that of the numerical model with/without DA for up to 42 hr with only 12 days of assimilation spin-up cycle. The symbolic equation generated from the proposed framework can be used to correct the predictions from WaveWatch III for weather prediction.